Question

Two point charges placed at a distance $r$ in the air experiences a certain force, then the distance at which they will experience the same force in the medium of dielectric constant $K$ is.

• A. $\frac{r}{K}$
• B. $Kr$
• C. $r\sqrt{K}$
• D. $\frac{r}{\sqrt{K}}$

Answer 1

The correct option is D $\frac{r}{\sqrt{K}}$

In the air medium,

$F=\frac{1}{4\pi {\epsilon }_0}\frac{q_1{q}_2}{r^2}$

In the medium with dielectric constant $K$,

$F^{\prime }=\frac{1}{4\pi {\epsilon }_{0}K}\frac{q_1{q}_2}{r_1^2}$

Given, $F^{\prime }=F$

$\frac{1}{K{r}_1^2}=\frac{1}{r^2}$

$r_1^2=\frac{r^2}{K}$

$\therefore r_1=\frac{r}{\sqrt{K}}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, (d) is the correct answer.